Both depend on temperature, and I'd say it's difficult to say which is less or more dependent on temperature.
In an enzyme catalysed reaction, the reaction can start without having reached the activation energy (because the enzyme catalyses), but the speed of the reaction depends on temperature (a dependence). And the enzyme itself also depends on temperature, as it has an optimum, where it works fastest (too high nothing works anymore when the protein is denatured, too low the speed is lowered to almost zero depending on enzyme; also a kind of dependence).
A spontaneous reaction depends on temperature first by activation energy that has to be high enough and also the reaction speed depends on temp.
So you have different types of dependence on temperature...

One must presume that long and short arguments contribute to the same end. - Epicurus...except casandra's that did belong to the funniest, most interesting and imaginative (or over-imaginative?) ones, I suppose.

All PCR reagent + Taq pol - try amplifying at different temperature- Perhaps at 60 o C and 90 oC you may not get amplification - More dependence on temperature

In theory even if you don't add enzymes reaction should proceed but when you compare it with enzyme dependent reaction - you have to wait for a long time.Your experiment face time constraints in this study.

you can study it provided that spontaneous reaction has feasible speed even in absence of enzyme.

You are right, what you are describing is seen using Arrhenius plots.
However, finding systems where you can directly compare enzyme vs non-enzymatic reactions directly is not always straight forward. The Arrhenius plots for enzymes are notoriously non-linear, as Hobgoblin was alluding to; the stability thermodynamics complicates the pure catalytic thermodynamics such that from a practical perspective the rate of an enzymatic reaction is more temperature dependent.